Question

Two concentric current loops lie in the same plane. The smaller loop has a radius of 3.8 cm and a current of 12 A . The bigger loop has a current of 20 A . The magnetic field at the center of the loops is found to be zero. Part A What is the radius of the bigger loop? Express your answer with the appropriate units. R R = nothing nothing SubmitRequest Answer Provide Feedback Next

Answer 1

Answer:

$R_2=6.33cm$

Explanation:

The equation for the magnetic field at the center of a circular loop is:

$B=\frac{\mu_0I}{2R}$

If we name the smaller loop as 1 and the bigger loop as 2 and we impose the same magnitude of the magnetic field at their center, we have:

$B_2=B_1$

$\frac{\mu_0I_2}{2R_2}=\frac{\mu_0I_1}{2R_1}$

$\frac{I_2}{R_2}=\frac{I_1}{R_1}$

$R_2=\frac{I_2}{I_1}R_1$

Which for our values means:

$R_2=\frac{I_2}{I_1}R_1=\frac{(20A)}{(12A)}(3.8cm)=6.33cm$

(Notice that we don't need to convert cm to m, we get our result in cm).